In commonly owned U.S. Pat. No. 3,777,532 there has been disclosed a method of and an apparatus for elongating and simultaneously thinning a sheet-metal band or strip under tension by deflecting that strip, alternately in opposite directions, around rollers of progressively smaller diameters. Such deflecting rollers are generally of slender shape since, on the one hand, they must extend over the full width of the sheet-metal strip and, on the other hand, they are to have a relatively small radius of curvature. It therefore becomes necessary to provide each deflecting roller with rotary supports engaging it over practically its entire length, advantageously in the form of two sets of shorter and heavier coaxially aligned back-up rollers held in closely spaced bearings. The machining and positioning of these bearings requires great precision inasmuch as deviations from exact alignment of adjacent back-up rollers may have a cumulative effect and can result in insufficient contact between the deflecting roller and its back-up rollers whereby, at the high rotary speed customary in such installations, the deflecting roller may break into oscillations leaving objectionable streaks or corrugations on the workpiece.